Water Quality Prediction under Changing Climate: An Uncertainty Quantification Approach for River Network Graphs

We introduce an uncertainty estimation approach coupling graph neural networks (GNN) with weighted conformal prediction to assess climate impacts on river water quality. Distribution shifts under non-stationary climate motivates a modelling approach to explicitly account for the differences between historical and future environmental conditions. Moreover, river connectivity carries information on cumulative impacts that should be taken into account. In our proposed approach, a GNN allows training under label-scarcity and leverages the network structure to reconstruct missing calibration errors by propagating information from observed to unobserved nodes. We equip the inference with weighted conformal correction that adjusts for distributional drift under non-stationary climate conditions. Our approach improved empirical coverage over historical data, returning an uncertainty adapted to local conditions ranging from headwater catchments to low-plain, highly anthropogenic basins. It demonstrates a good practice in water quality modeling, particulary for uncertainty quantification under future climate conditions.